Franck-Hertz Experiment

The discreteness of atomic energy levels was first shown directly in the Franck-Hertz experiment. This experiment is one of the classic demonstrations of the quantization of atomic energy levels and was first performed by J. Frank and G. Hertz in 1914. Their goal was to verify the quantum theory assumptions about the existence of discrete energy levels in atoms and that quantized amounts of energy are transferred in emission and absorption.

By accelerating a beam of electrons through a mercury vapor, they found that when the kinetic energy of the electrons reached about 4.9 eV, the vapor emitted a spectrum line at 254 nm. This experiment led to the detailed investigation of the atomic structure of many elements. When an electron encounters an atom and bounces off without losing any of its energy then such an event is called an “elastic scattering”. The electron will be elastically scattered unless it has sufficient energy to cause a change in the internal energy of the atom.

Since atomic energy levels are quantized, this means that electrons flowing through a gas of atoms with less energy than the first excited state of the atoms will not lose any energy as they travel. On the other hand, an electron with enough energy to cause a transition to an excited state of the atom may induce such a transition with subsequent loss of kinetic energy. Such an event is called an “inelastic scattering” of the electron by the atom.

In the Franck Hertz experiment electrons are emitted from a hot cathode into a tube filled with mercury vapor. The experimental arrangement is shown in figure below.

The driving potential Vg₁ reduces the space charge and causes a large current to flow in the tube. The electrons are then accelerated through a positive potential by the accelerating potential Vg₂.

After being accelerated, the electrons are slowed by a potential drop in the opposite direction by the braking potential. Then the electrons are collected at a far end of the tube and the current is measured. In a vacuum tube that contains no gas the current would rise steadily as the accelerating voltage Vg₂, is increased. The presence of the gas changes this behavior because of collisions of the electrons with the gas atoms. At first the current does rise with the potential, but when the electrons get enough energy they inelastically collide with the gas atoms and excite higher energy levels in the gas.

After these collisions the electrons will have lower energy and due to the opposing potential, they will not make it to the end of the tube. This will cause the current to decrease to a minimum. After this minimum, as the potential increases the current will again increase until the electrons get enough energy to excite the gas twice. This process continues with the electrons repeatedly exciting the gas atoms. The potential difference between the minima (or maxima) is equivalent to the energy of the excited level. The graph plotted between the accelerating potential and anode current is shown below.

At each of the critical potentials (V­₁, V_2, or V₃ etc.) the electrons have just sufficient kinetic energy to raise the internal energy of the sodium atom by collision.